Question

which transformation would take figure a to figure b? graph of coordinate plane with figure a (pink) and figure b (blue) shown answer: a clockwise rotation of 270° about the origin; a clockwise rotation of 90° about the origin; a reflection over the y - axis; a reflection over the x - axis

Explanation:

Step1: Analyze Reflection Over Y - Axis

A reflection over the \( y \) - axis changes the sign of the \( x \) - coordinate of a point \((x,y)\) to \((-x,y)\). Let's take a vertex of Figure A, say if a vertex of A is \((a,b)\), after reflection over \( y \) - axis, it becomes \((-a,b)\). By observing the coordinates of the vertices of Figure A and Figure B, we can see that the \( x \) - coordinates of the vertices of A are positive and those of B are negative (while \( y \) - coordinates remain the same in terms of sign pattern).

Step2: Eliminate Other Options

• For a clockwise rotation of \( 90^{\circ} \) about the origin, the transformation rule is \((x,y)\to(y, - x)\). This would change the coordinates in a way that doesn't match the relationship between A and B.
• For a clockwise rotation of \( 270^{\circ} \) about the origin, the transformation rule is \((x,y)\to(-y,x)\), which also doesn't match the coordinate relationship.
• For a reflection over the \( x \) - axis, the transformation rule is \((x,y)\to(x, - y)\), which would flip the figure vertically, but Figure A and B are flipped horizontally, not vertically.

Answer:

A reflection over the y - axis